In a summer when the president is traveling across the country meeting with ordinary Americans under highly choreographed conditions, the Rome dinner shows another side of Mr. Obama. As one of an increasing number of late-night dinners in his second term, it offers a glimpse into a president who prefers intellectuals to politicians, and into the rarefied company Mr. Obama may keep after he leaves the White House.

Sometimes stretching into the small hours of the morning, the dinners reflect a restless president weary of the obligations of the White House and less concerned about the appearance of partying with the rich and celebrated. Freewheeling, with conversation touching on art, architecture and literature, the gatherings are a world away from the stilted meals Mr. Obama had last year with Senate Republican leaders at the Jefferson Hotel in Washington.

In Paris, the president was up again until nearly midnight enjoying, among other things, Drappier Champagne.

“Bonsoir,” Mr. Obama said as he entered the small Restaurant Helen, according to Frédéric Pescatori, an investment manager who was dining next to the president’s party. Mr. Pescatori added that the president “seemed quite relaxed and glad to be with friends, without stress.”